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Net Present Value rule (NPV) NPV is the present value of a project minus its cost If NPV is greater than zero, the firm should go ahead to invest; otherwise forget about this project A hidden assumption: there is no budget constraint or money constraint.

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NPV (continue) In other words: Managers can increase shareholders’ wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value if there is no budget constraint.

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Net Present Value NPV = PV - required investment

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Net Present Value Example You have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building?

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Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

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Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

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Another example about NPV An oil well, if explored, can now produce 100,000 barrels per year. The well will produce forever, but production will decline by 4% per year. Oil prices, however, will increase by 2% per year. The discount rate is 8%. Suppose that the price of oil now is $14 for barrel. If the cost of oil exploration is $12.8 million, do you want to take this project?

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IRR rule Internal Rate of Return (IRR) – Single discount rate at which NPV = 0. IRR rule - Invest in any project offering a IRR that is higher than the opportunity cost of capital or the discount rate.

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IRR rule Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

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Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

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Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? IRR = 12.96%

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Internal Rate of Return IRR=12.96%

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What’s wrong with IRR? Pitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem. Example You have two proposals to choose between. The initial proposal (H) has a cash flow that is different from the revised proposal (I). Using IRR, which do you prefer?

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Internal Rate of Return (1) Example You have two proposals to choose between. The initial proposal (H) has a cash flow that is different from the revised proposal (I). Using IRR, which do you prefer?

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What’s wrong with IRR (3)? Pitfall 3 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates. The following cash flow generates NPV=0 at both (- 50%) and 15.2%. Example A project costs $1000 and produces a cash flow of $800 in year 1, a cash flow of $150 every year from year 2 to year 5, and a cash flow of -150 in year 6.

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Payback period rule Payback period is the number of periods such that cash flows recover the initial investment of the project. The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this rule.

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Payback period rule The following example shows that all the three projects have a payback period of 2. If the payback period used by the firm is 2, the firm can take project C and lose money. Cash Flows Prj. C 0 C 1 C 2 C 3 Payback A ,429 B C

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Example A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income.

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Solution (using accounting profit)

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Solution (using cash flows)

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Forget about financing When valuing a project, ignore how the project is financed. You can assume that the firm is financed by issuing only stocks; or the firm has no debt but just equity

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Incremental cash flows Incremental cash flows are the increased cash flows due to investment Do not get confused about the average cost or total cost? Do you have examples about incremental costs? Incremental Cash Flow cash flow with project cash flow without project = -

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Working capital Working capital is the difference between a firm’s short-term assets and liabilities. The principal short-term assets are cash, accounts receivable, and inventories of raw materials and finished goods. The principal short-term liabilities are accounts payable. The change in working capital represents real cash flows and must be considered in the cash flow calculation

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Example We know that inventory is working capital. Suppose that inventory at year 1 is $10 m, and inventory at year 2 is $15. What is the change in working capital? Why does this change represent real cash flows?

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Sunk costs The sunk cost is past cost and has nothing to do with your investment decision Is your education cost so far at SFSU is sunk cost?

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Opportunity cost The cost of a resource may be relevant to the investment decision even when no cash changes hands. Give me an example about the opportunity cost of studying at SFSU?

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Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows. Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures Inflation rule

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Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

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Inflation Example - nominal figures

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Inflation Example - real figures

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How to calculate free cash flows? Free cash flows = cash flows from operations + cash flows from the change in working capital + cash flows from capital investment and disposal We can have three methods to calculate cash flows from operations, but they are the exactly same, although they have different forms.